Difference between revisions of "2015 AMC 8 Problems/Problem 24"
Crocodile 40 (talk | contribs) (→Solution 2) |
(→Solution 1) |
||
Line 8: | Line 8: | ||
\textbf{(E) } 72 | \textbf{(E) } 72 | ||
</math> | </math> | ||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
===Solution 2=== | ===Solution 2=== |
Revision as of 20:47, 15 June 2016
A baseball league consists of two four-team divisions. Each team plays every other team in its division games. Each team plays every team in the other division games with and . Each team plays a 76 game schedule. How many games does a team play within its own division?
Solution 2
On one team they play games in their division and games in the other. This gives
Since we start by trying . This doesn't work because is not divisible by .
Next , does not work because is not divisible by
We try this does work giving and thus games in their division.
Solution 3
, giving . Since , we have Since is , we must have equal to , so .
This gives , as desired. The answer is .
See Also
2015 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 23 |
Followed by Problem 25 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.